The Norway midfielder has joined on-loan from Real Madrid.
"He's a player that we followed for some time and we believe that he's got some special qualities that we need, that we have been missing," said Arteta.
"Now we have to give him a little bit of time. He hasn't played that many minutes in Madrid but he's been training hard and he looks so excited, as we are, to have another big talent at our club.
"I think in the last few seasons he's progressed and developed in the right way. I've followed him very closely because he played for Real Sociedad, which is my home town. I know him really well.
"I've been really impressed. He's a such a talent. He needs the right environment, he needs a little bit of time but I think he's got the qualities to be a success for us."
So where does Arteta see Odegaard making the most impact in his side?
"He's a specialist to play in the pockets, to play in the No 8 or 10 positions," he said. "He can play off the sides. He's a really creative player who's really comfortable on the ball in tight spaces.
"He has the capacity to create chances and to score goals. Something that he has improved a lot is his workrate without the ball as well, so it's another option to give us more creativity for sure in the final third, and give us more options to set up in different ways against certain teams."
Asked if Odegaard will start against Manchester United on Saturday, Arteta was coy.
"It's a little bit early to decide. Let's see how he goes in training and we will see, don't worry."